Theorem ancld 308

Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 1-Nov-2012.)

Hypothesis

Ref	Expression
ancld.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
ancld	⊢ (φ → (ψ → (ψ ∧ χ)))

Proof of Theorem ancld

Step	Hyp	Ref	Expression
1		idd 21	. 2 ⊢ (φ → (ψ → ψ))
2		ancld.1	. 2 ⊢ (φ → (ψ → χ))
3	1, 2	jcad 291	1 ⊢ (φ → (ψ → (ψ ∧ χ)))

Syntax hints:   → wi 4   ∧ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101

This theorem is referenced by:  mopick2  1965  cgsexg  2566  cgsex2g  2567  cgsex4g  2568  reximdva0m  3213  difsn  3475  preq12b  3515  elres  4573  relssres  4575  fnoprabg  5525  1idprl  6429  1idpru  6430